Question

question
what is the equation of the line that passes through the point (6,2) and has a slope of \\(\frac{1}{3}\\)?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 6$, $y_1=2$ and $m=\frac{1}{3}$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 6$, $y_1 = 2$ and $m=\frac{1}{3}$ into the point - slope formula:
$y - 2=\frac{1}{3}(x - 6)$

Step3: Simplify the equation

First, distribute $\frac{1}{3}$ on the right - hand side:
$y - 2=\frac{1}{3}x-2$
Then, add 2 to both sides of the equation:
$y=\frac{1}{3}x-2 + 2$
$y=\frac{1}{3}x$

Answer:

The equation of the line is $y=\frac{1}{3}x$ (or in standard form $x - 3y = 0$)